A Physical Interpretation of the Modal Mass in Structural Dynamics

The magnitude and the units of the modal mass of a mode shape is not unique but it depends on the normalization method used to define the mode shape. Moreover, the magnitude can also depend depends on the number of degrees of freedom (DOFs) used to discretize the model. Recently, a new definition of the length of a mode shape, which depends on the mode shape and how the volume is distributed in the structure, has been proposed by the authors. This definition allows a better definition of the modal mass, which is physically meaningful and does not depend on the number of DOFs of a discrete model. With this new definition, the modal mass in constant mass-density systems is equal to the product between the total mass of the structure and the length squared. This property can be used advantageously to validate the modal masses estimated with the techniques proposed by different authors to determine the modal masses in operational modal analysis. In this paper, these new concepts are explained by analytical, numerical, and experimental examples. The model masses of an experimental steel beam structure were estimated by experimental modal analysis and validated with the equations proposed in this paper. Moreover, the modal masses and lengths of a rigid beam supported on two springs, were calculated using different sets of DOF’s and different types of normalization, demonstrating that the same mass normalized mode shapes are obtained.